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Surface Area of Rectangular Prism

Like a cube, a rectangular prism also has six sides, but its opposite sides have the same area. So it has three sets of 2 faces each that have the same area.

Let us look at a rectangular prism below. ‘Opening up’ this rectangular prism will produce a net. A net is a flat diagram that contains the faces of a solid shape. The faces are arranged so that the diagram could be folded to form that solid (in this case, a rectangular prism). Drawing the net of a prism can help with calculating the surface area.

surface area of a rectangular prism_1

The surface area of a rectangular prism is the sum of the areas of the three sets of rectangular faces with the same area.

Surface area = (area of bottom face x 2) + (area of right face x 2) + (area of front face x 2)

=  (l x b x 2)  +  (b x h x 2)  +  (l x h x 2)

=  2(lb + bh + lh)

 

Example 1 : Calculate the surface area of the rectangular prism here by first sketching a net diagram.

surface area of a rectangular prism_2

Surface area = (area of bottom face x 2) + (area of right face x 2) + (area of front face x 2)

=  (7 x 5 x 2)  +  (5 x 3 x 2)  +  (7 x 3 x 2)

=  70 + 30 + 42

=  142 cm2

 

Example 2 : For the rectangular prism shown here, sketch a net diagram, and then calculate the surface area.

surface area of a rectangular prism_3

Surface area = (area of bottom face x 2) + (area of right face x 2) + (area of front face x 2)

=  2(14 x 11)  +  2(11 x 8)  +  2(14 x 8)

=  2 x 154  +  2 x 88  +  2 x 112

=  308 + 176 + 224

=  708 cm2

 

Example 3 : Calculate the surface area of a rectangular prism with dimensions: length = 80 mm, breadth = 45 mm, and height = 25 mm.

Surface area  =  2 (lb + bh + lh)

=  2 (80 x 45  +  45 x 25  +  80 x 25)

=  2 (3600 + 1125 + 2000)

=  2 x 6725

=  13,450 mm2

 

Here are some more examples of area of prisms.